In the design of new structures and assessment of existing structures, short- and long term statistical distributions of wave height, crest height and wave periods, as well as joint distributions, are important for structural integrity assessment. It is important to model the statistical distributions accurately to calculate wave design criteria and to assess fatigue life.

A detailed study of the wave statistics for an offshore location at the Norwegian Continental Shelf field is carried out. Extensive time domain simulations for the complete scatter diagram of possible sea states are carried out by a second order wave model. Time series of the surface elevation are generated for JONSWAP and Torsethaugen wave spectra, and for several wave spreading models. Statistics for individual wave heights, crest heights and wave periods are established. The simulated results for the short-term statistics are compared with existing short term models that are commonly used, viz. the Forristal, Næss and Rayleigh wave height distributions, and the Forristall 2nd order crest height distribution. Also, parameterized distributions for wave height and for crest height are fitted to the simulated data.

The long-term distributions F(H) and F(C) of all simulated individual wave heights H and crest heights C are determined by weighting the simulations with the long-term probability of occurrence of the sea state. Likewise, the long-term distributions F(Hmax) and F(Cmax) of the maximum simulated individual wave heights Hmax and crest heights Cmax in the sea states are determined.

The design criteria for return periods R = 1, 10, 100 and 10 000 years are determined from the appropriate quantile levels.

The effect of statistical uncertainty is investigated by comparing the confidence intervals for the estimated extreme values results as function of the number N of 3-hour time domain simulations per sea state for 10<N<500.

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